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The Mathematics of Mixing

Although audio mixing has always been viewed as the artistic task of either a conductor balancing the musicians in a live performance or a mixing engineer combining multiple tracks in a sound studio, this research considers mixing as a mathematical optimization problem. Using an auditory model, the authors demonstrated how numerical optimization can be used to pose and solve a mix problem. There is interplay between artistic objectives, perceptual constraints, and engineering methods. Taking loudness as an example, it is shown that the nonlinearity in the perceptual model leads to complex behavior, which can be overcome by careful choice of optimization strategies and parameters.